Single Fuzzy Approximator Based Stabilization Control With Multi-uncertainties: A Discrete-Time Prescribed Performance Approach

This article focuses on fuzzy prescribed performance stabilization of high-order discrete-time systems with multiple unknown nonlinearities. A novel back-steeping framework is employed to devise the unique actual control protocol, while the series of virtual controllers associated with the existing back-stepping are not necessary for the proposed approach. Furthermore, as to the considered high-order system whose subsystems contain unknown dynamics, only one fuzzy approximator is used to directly estimate the final control law. This results in a low-computational model-free design procedure. In particular, a finite-time performance function is developed to sustain the system output within a constraint envelope to satisfy the desired prescribed performance in the discrete-time domain. Finally, the stability of a closed-loop system and the reachability of prescribed performance are proved via Lyapunov synthesis, and the efficiency of the explored method is verified via numerical simulation.